{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   distance  accuracy\n",
      "0  0.314379 -0.707727\n",
      "1  1.693777 -1.586669\n",
      "2 -0.059695 -0.176699\n",
      "3 -0.574047  0.372640\n",
      "4  1.343083 -1.934584\n"
     ]
    },
    {
     "data": {
      "image/png": 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xsy5gbGxsjK6urqyLIxFt2HAWo6O7mJ29mvkV4qpDaa/TrNTjSB2epf379/stLemkLReR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\nnQIMERERid3/D4/OWOVd9BdWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20bfb438908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Read data from csv\n",
    "pga = pandas.read_csv(\"pga.csv\")\n",
    "\n",
    "\n",
    "# Normalize the data\n",
    "pga.distance = (pga.distance - pga.distance.mean()) / pga.distance.std()\n",
    "pga.accuracy = (pga.accuracy - pga.accuracy.mean()) / pga.accuracy.std()\n",
    "print(pga.head())\n",
    "\n",
    "plt.scatter(pga.distance, pga.accuracy)\n",
    "plt.xlabel('normalized distance')\n",
    "plt.ylabel('normalized accuracy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the series: (197,)\n",
      "Shape with newaxis: (197, 1)\n",
      "-0.607598822715\n"
     ]
    }
   ],
   "source": [
    "# accuracyi=θ1distancei+θ0+ϵ\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import numpy as np\n",
    "\n",
    "# We can add a dimension to an array by using np.newaxis\n",
    "print(\"Shape of the series:\", pga.distance.shape)\n",
    "print(\"Shape with newaxis:\", pga.distance[:, np.newaxis].shape)\n",
    "\n",
    "# The X variable in LinearRegression.fit() must have 2 dimensions\n",
    "lm = LinearRegression()\n",
    "lm.fit(pga.distance[:, np.newaxis], pga.accuracy)\n",
    "theta1 = lm.coef_[0]\n",
    "print (theta1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5994384226\n"
     ]
    },
    {
     "data": {
      "image/png": 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8jhOQ4uPjiY6OBoh2zsX7s63fpw/SCkFD4LYzFYI0XwK1TlhWN215jtei9nXc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8172ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The cost function of a single variable linear model\n",
    "def cost(theta0, theta1, x, y):\n",
    "    # Initialize cost\n",
    "    J = 0\n",
    "    # The number of observations\n",
    "    m = len(x)\n",
    "    # Loop through each observation\n",
    "    for i in range(m):\n",
    "        # Compute the hypothesis \n",
    "        h = theta1 * x[i] + theta0\n",
    "        # Add to cost\n",
    "        J += (h - y[i])**2\n",
    "    # Average and normalize cost\n",
    "    J /= (2*m)\n",
    "    return J\n",
    "\n",
    "# The cost for theta0=0 and theta1=1\n",
    "print(cost(0, 1, pga.distance, pga.accuracy))\n",
    "\n",
    "theta0 = 100\n",
    "theta1s = np.linspace(-3,2,100)\n",
    "costs = []\n",
    "for theta1 in theta1s:\n",
    "    costs.append(cost(theta0, theta1, pga.distance, pga.accuracy))\n",
    "\n",
    "plt.plot(theta1s, costs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
      "         -9.19191919],\n",
      "       [-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
      "         -9.19191919],\n",
      "       [-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
      "         -9.19191919],\n",
      "       [-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
      "         -9.19191919],\n",
      "       [-10.        ,  -9.7979798 ,  -9.5959596 ,  -9.39393939,\n",
      "         -9.19191919]]), '\\n', array([[-10.        , -10.        , -10.        , -10.        , -10.        ],\n",
      "       [ -9.7979798 ,  -9.7979798 ,  -9.7979798 ,  -9.7979798 ,  -9.7979798 ],\n",
      "       [ -9.5959596 ,  -9.5959596 ,  -9.5959596 ,  -9.5959596 ,  -9.5959596 ],\n",
      "       [ -9.39393939,  -9.39393939,  -9.39393939,  -9.39393939,\n",
      "         -9.39393939],\n",
      "       [ -9.19191919,  -9.19191919,  -9.19191919,  -9.19191919,\n",
      "         -9.19191919]]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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X2+1m5cqVzXrB2rxn3RZOaHlL0yI2V6c+nw+3242u6zidToqKisjKygq+tilaH4YTup9t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\nbNjiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x82b2350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oAjbFMO6hvX099thjT6655pqKxiz7K9XMfLYnkClPUnNzM83NzencERWCUKNT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3SKthxyGJjNINxgCI/H08QKd6LYTIVCOp4hFRD6MhoRiVFOV1ZWBgVZ1g3NDF83eeJMNknwer1M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\nIYSQKAB/BZBs0MkzGCbE/wNUPO4whKGj9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x82dead0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Example of a Surface Plot using Matplotlib\n",
    "# Create x an y variables\n",
    "x = np.linspace(-10,10,100)\n",
    "y = np.linspace(-10,10,100)\n",
    "\n",
    "# We must create variables to represent each possible pair of points in x and y\n",
    "# ie. (-10, 10), (-10, -9.8), ... (0, 0), ... ,(10, 9.8), (10,9.8)\n",
    "# x and y need to be transformed to 100x100 matrices to represent these coordinates\n",
    "# np.meshgrid will build a coordinate matrices of x and y\n",
    "X, Y = np.meshgrid(x,y)\n",
    "#print(X[:5,:5],\"\\n\",Y[:5,:5])\n",
    "\n",
    "# Compute a 3D parabola \n",
    "Z = X**2 + Y**2 \n",
    "\n",
    "# Open a figure to place the plot on\n",
    "fig = plt.figure()\n",
    "# Initialize 3D plot\n",
    "ax = fig.gca(projection='3d')\n",
    "# Plot the surface\n",
    "ax.plot_surface(X=X,Y=Y,Z=Z)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "# Use these for your excerise \n",
    "theta0s = np.linspace(-2,2,100)\n",
    "theta1s = np.linspace(-2,2, 100)\n",
    "COST = np.empty(shape=(100,100))\n",
    "# Meshgrid for paramaters \n",
    "T0S, T1S = np.meshgrid(theta0s, theta1s)\n",
    "# for each parameter combination compute the cost\n",
    "for i in range(100):\n",
    "    for j in range(100):\n",
    "        COST[i,j] = cost(T0S[0,i], T1S[j,0], pga.distance, pga.accuracy)\n",
    "\n",
    "# make 3d plot\n",
    "fig2 = plt.figure()\n",
    "ax = fig2.gca(projection='3d')\n",
    "ax.plot_surface(X=T0S,Y=T1S,Z=COST)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('partial1 =', 5.5791338540718973)\n"
     ]
    }
   ],
   "source": [
    "def partial_cost_theta1(theta0, theta1, x, y):\n",
    "    # Hypothesis\n",
    "    h = theta0 + theta1*x\n",
    "    # Hypothesis minus observed times x\n",
    "    diff = (h - y) * x\n",
    "    # Average to compute partial derivative\n",
    "    partial = diff.sum() / (x.shape[0])\n",
    "    return partial\n",
    "\n",
    "partial1 = partial_cost_theta1(0, 5, pga.distance, pga.accuracy)\n",
    "print(\"partial1 =\", partial1)\n",
    "# Partial derivative of cost in terms of theta0\n",
    "def partial_cost_theta0(theta0, theta1, x, y):\n",
    "    # Hypothesis\n",
    "    h = theta0 + theta1*x\n",
    "    # Difference between hypothesis and observation\n",
    "    diff = (h - y)\n",
    "    # Compute partial derivative\n",
    "    partial = diff.sum() / (x.shape[0])\n",
    "    return partial\n",
    "\n",
    "partial0 = partial_cost_theta0(1, 1, pga.distance, pga.accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Theta1 =', -0.60469831663796081)\n"
     ]
    },
    {
     "data": {
      "image/png": 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CmNbsCmhy6OjooLPzQB599FUMTDu9Lj97BP39W5tXOUnShGGLhUZt3rwDgZ0MNe306aef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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6554850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x is our feature vector -- distance\n",
    "# y is our target variable -- accuracy\n",
    "# alpha is the learning rate\n",
    "# theta0 is the intial theta0 \n",
    "# theta1 is the intial theta1\n",
    "def gradient_descent(x, y, alpha=0.1, theta0=0, theta1=0):\n",
    "    max_epochs = 1000 # Maximum number of iterations\n",
    "    counter = 0      # Intialize a counter\n",
    "    c = cost(theta1, theta0, pga.distance, pga.accuracy)  ## Initial cost\n",
    "    costs = [c]     # Lets store each update\n",
    "    # Set a convergence threshold to find where the cost function in minimized\n",
    "    # When the difference between the previous cost and current cost \n",
    "    #        is less than this value we will say the parameters converged\n",
    "    convergence_thres = 0.000001  \n",
    "    cprev = c + 10   \n",
    "    theta0s = [theta0]\n",
    "    theta1s = [theta1]\n",
    "\n",
    "    # When the costs converge or we hit a large number of iterations will we stop updating\n",
    "    while (np.abs(cprev - c) > convergence_thres) and (counter < max_epochs):\n",
    "        cprev = c\n",
    "        # Alpha times the partial deriviative is our updated\n",
    "        update0 = alpha * partial_cost_theta0(theta0, theta1, x, y)\n",
    "        update1 = alpha * partial_cost_theta1(theta0, theta1, x, y)\n",
    "\n",
    "        # Update theta0 and theta1 at the same time\n",
    "        # We want to compute the slopes at the same set of hypothesised parameters\n",
    "        #             so we update after finding the partial derivatives\n",
    "        theta0 -= update0\n",
    "        theta1 -= update1\n",
    "        \n",
    "        # Store thetas\n",
    "        theta0s.append(theta0)\n",
    "        theta1s.append(theta1)\n",
    "        \n",
    "        # Compute the new cost\n",
    "        c = cost(theta0, theta1, pga.distance, pga.accuracy)\n",
    "\n",
    "        # Store updates\n",
    "        costs.append(c)\n",
    "        counter += 1   # Count\n",
    "\n",
    "    return {'theta0': theta0, 'theta1': theta1, \"costs\": costs}\n",
    "\n",
    "print(\"Theta1 =\", gradient_descent(pga.distance, pga.accuracy)['theta1'])\n",
    "descend = gradient_descent(pga.distance, pga.accuracy, alpha=.01)\n",
    "plt.scatter(range(len(descend[\"costs\"])), descend[\"costs\"])\n",
    "plt.show()"
   ]
  },
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   "outputs": [],
   "source": []
  }
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